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[tex]if \: the \: volume \: of \: a \: box \: (in \: cubic \: inches) \: cn \: be \: expressed \: as \: v(x) = 5x { }^{3} + 12x {}^{2} - 71x - 30.find \: the \: length \: if \: the \: width \: (x+5) \: inches \: and \: the \: heigth \: is \: (x - 3)inches. \\ \\ \\ show \: solution[/tex]

Sagot :

Answer:

5x + 2 inches

Step-by-step explanation:

[tex]\rm V = lwh[/tex]

Given:

  • [tex]\rm V(x) = 5x^3 + 12x^2 - 71x - 30[/tex]
  • [tex]\rm w = x + 5[/tex]
  • [tex]\rm h = x-3[/tex]

[tex]\implies \rm 5x^3 + 12x^2 -71x - 30 = l(x+5)(x-3)[/tex]

[tex]\implies \rm l = \frac{5x^3 + 12x^2 - 71x - 30}{(x+5)(x-3)}[/tex]

[tex]\implies \rm l = \frac{(5x+2)(x+5)(x-3)}{(x+5)(x-3)}[/tex]

[tex]\implies \boxed{\rm l = 5x+2 \ inches}[/tex]

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